Rewrite as a simplified fraction. ${2.\overline{17} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 217.1717...\\ 1x &= 2.1717...\end{align*}}$ Subtracting the two equations, we have: ${99x = 215}$ ${x = \dfrac{215}{99}} \text{or} {2 \dfrac{17}{99}}$